Answer: undefined, 0, -1, -2.5
Slope formula: rise over run OR (y1 - y2)/(x1 - x2)
The slope formula asks you to take two corresponding y values and x values, find their difference, and divide.
Example: Find the slope of (a, b) and (c, d)
The slope would be (a - c)/(b-d) OR (c - a)/(d - b).
It doesn't really matter which order you subtract the y-values as long as you do the same for the x-values, and vice versa.
Number 10:
Remember that a vertical line is an undefined slope!
Vertical lines increase in the y-axis, but not in the x-axis. To calculate slope you need to find the rise (y increase/decrease) over run (x increase/decrease).
So basically, the y increases forever (infinity), and is divided by 0 because the x value never increases- and you cannot divide anything by zero! You can look into why- there is a really good TedEd video I can link for you if you need it.
Therefore, the slope is undefined.
Number 11:
Straight horizontal lines always have a slope of 0- don't confuse them with vertical lines!
The rise is 0 and the run, or how much the y value increases, is infinity, because it goes on forever. 0 divided by any value other than zero is equal to zero, so the slope would be zero.
Number 12:
Right away, you can tell that this is a negative slope because it is going down on the right side of the graph! So if you don't get a negative value as your slope, you know to check your calculations.
The coordinates that are indicated by circles on the graph are (3, 4) and (4, 3).
The slope formula: (y1 - y2)/(x1 - x2)
I'll use the first point to be (x1, y1) and the second to be the values of (x2, y2)
(4 - 3)/(3 - 4) = (1)/(-1)
One divided by negative one is equal to negative 1! If you need a refresher on how to subtract or divide with negative numbers, there are a lot of great resources for that too.
So, the slope is negative 1.
Number 13:
Once again, this is a negative slope. The y values are decreasing as the x values are increasing.
The coordinates that are highlighted on the graph are (0, 4) and (3, -3).
The slope formula: (y1 - y2)/(x1 - x2)
This time, let's switch it up- I'll use the first point to be (x2, y2) and the second to be the values of (x1, y1):
(-3 - 4)/(3 - 0) = (-7)/(3)
Negative seven divided by positive three is negative 2.5.
So, the slope is negative 2.5.
I know that learning this topic can be really overwhelming, I struggled a lot with it at first- so I'm really proud you took the time to reach out and ask for explanations! I hope this helped you! Let me know if you have any questions.
